From the early Church Fathers to now.
We praise thee, O God: we acknowledge thee to be the Lord. All the earth doth worship thee: the Father everlasting. To thee all Angels cry aloud: the Heavens, and all the Powers therein. To thee Cherubim and Seraphim: continually do cry, Holy, Holy, Holy: Lord God of Sabaoth; Heaven and earth are full of the Majesty: of thy glory.
A cherished tradition holds that Ambrose and Augustine composed and sang the Te Deum alternately, extempore, on the night of Augustine's baptism. The Catholic Encyclopedia notes this account "can be traced back to the end of the eighth century" — long after the event, and marks it as legend rather than history.
Among the names to which the hymn has been ascribed, modern scholarship has increasingly favoured Nicetas, Bishop of Remesiana (in present-day Serbia), a contemporary of Ambrose.
The hymn — under its opening words, Te Deum Laudamus — appears by name in the Rule of St. Caesarius of Arles for monks, its earliest known title, giving firm witness to its use in the early sixth century.
“But neither to Hilary nor to Ambrose may the hymn be prudently ascribed, because although both composed hymns, the Te Deum is in rhythmical prose, and not in the classical metres of the hymns known to have been written by them.”
The in-app commentary runs from the Fathers to the early-modern record, then stops — that's where the public-domain sources end, not where the reading does. For the modern reading, follow the sources directly.